f(x)=3sinx-2cosx >sin function
2010-03-11 4:38 am
f(x)=3sinx-2cosx.show f can be written as a sine function which hv been shifted horizontally,then stretched vertically.find the amplitude of f
回答 (1)
2010-03-11 5:41 am
✔ 最佳答案
f(x) = 3 sin x - 2 cos x = A sin( x - b) = A cos b sinx - A sin b cos x.so 3 = A cos b .... (1) and
2 = A sin b ......(2)
Squaring and adding the 2 equations we get
3^2 + 2^2 = (A cos b)^2 + (A sin b)^2 = A^2( cos^2 b + sin^2 b) = A^2
so 9 + 4 = A^2
A = amplitude = sqrt 13.
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